Distinguishable dyads

Adding gender (or any distinguishing variable) to the APIM

When the two members of each dyad can be told apart — by gender, role, age, or any other stable marker — the actor and partner slopes are no longer forced to be equal. You can then ask whether the difference between actor and partner slopes is itself a substantively interesting quantity, and you can test whether gender moderates any of the actor or partner effects.

The four tutorials in this section cover the three standard ways to fit a distinguishable APIM in R.

Tutorial 04 — Distinguishable dyads: MLM moderator

Long format, lme4::lmer. Add gender as a moderator of every actor and partner effect. Simple slopes. Likelihood ratio test for the gender × predictor interaction block.

MLM + gender Intermediate

Open tutorial →

Tutorial 05 — Distinguishable dyads: SEM with moderation

Long format, lavaan. Manual interaction columns. Two-level SEM with the within-dyad interactions and the between-dyad moderators. Calculated simple slopes.

SEM + gender Advanced

Open tutorial →

Tutorial 06 — Distinguishable dyads: SEM wide

Wide format, lavaan. The three-model sequence: unconstrained, slopes-equal, fully constrained. The three nested likelihood ratio tests. The Olsen & Kenny (2006) indistinguishability test.

SEM wide Advanced

Open tutorial →

Tutorial 07 — Two-intercept models

Long format, lme4::lmer. The parameterisation trick: suppress the global intercept, replace it with two role-specific intercepts. Its SEM analogue in wide format.

Two-intercept Intermediate

Open tutorial →

How the four tutorials relate

The four approaches give you the same quantities — actor and partner slopes, separated by role — but they package the model differently.

MLM moderator (04). A single long-format model. Gender is a factor that interacts with every predictor. The intercept is the reference-group (male) intercept; the female intercept is the reference + the gender main effect.
SEM with moderation (05). The same idea in lavaan. Manual interaction columns make the within-dyad level of the model transparent. The two-level specification places the gender interactions at the within-dyad level and the dyad-level moderators at the between-dyad level.
SEM wide (06). Wide format, with separate paths for the two roles. The three-model sequence (unconstrained → slopes-equal → fully constrained) is the classical Olsen & Kenny (2006) indistinguishability test.
Two-intercept (07). A special parameterisation that estimates both intercepts directly (rather than as reference + main effect). Useful when you want to report absolute group means.

The MLM and SEM specifications should give you nearly identical estimates. The MLM is usually easier to read; the SEM gives you fit indices and the k-pattern tests for free.

A note on the data

The dyad_data.RData dataset has a single DGP-level gender difference: a 0.15-point gap in the male and female intercepts ($\alpha_m = 5.00$, $\alpha_f = 4.85$). The actor and partner slopes are equal across gender in the DGP. This means:

The MLM moderator likelihood ratio test should not reject the null of no gender × predictor interaction.
The SEM wide slope-equality test should be non-significant.
The SEM wide intercept-equality test should be significant, because the male and female intercepts differ by 0.15.

This is the standard empirical pattern: dyad members are distinguishable by means but not by effects. The two-intercept tutorial is the recommended specification for this case.

--- title: "Distinguishable dyads" subtitle: "Adding gender (or any distinguishing variable) to the APIM" --- When the two members of each dyad can be told apart — by gender, role, age, or any other stable marker — the actor and partner slopes are no longer forced to be equal. You can then ask whether the *difference* between actor and partner slopes is itself a substantively interesting quantity, and you can test whether gender moderates any of the actor or partner effects. The four tutorials in this section cover the three standard ways to fit a distinguishable APIM in R. ::: {.card-grid} ::: {.card} ### [Tutorial 04 — Distinguishable dyads: MLM moderator]{.card-title-link} Long format, `lme4::lmer`. Add `gender` as a moderator of every actor and partner effect. Simple slopes. Likelihood ratio test for the gender × predictor interaction block. MLM + gender Intermediate [Open tutorial →](mlm-moderator.html) ::: ::: {.card} ### [Tutorial 05 — Distinguishable dyads: SEM with moderation]{.card-title-link} Long format, `lavaan`. Manual interaction columns. Two-level SEM with the within-dyad interactions and the between-dyad moderators. Calculated simple slopes. SEM + gender Advanced [Open tutorial →](sem-moderation.html) ::: ::: {.card} ### [Tutorial 06 — Distinguishable dyads: SEM wide]{.card-title-link} Wide format, `lavaan`. The three-model sequence: unconstrained, slopes-equal, fully constrained. The three nested likelihood ratio tests. The Olsen & Kenny (2006) indistinguishability test. SEM wide Advanced [Open tutorial →](sem-wide.html) ::: ::: {.card} ### [Tutorial 07 — Two-intercept models]{.card-title-link} Long format, `lme4::lmer`. The parameterisation trick: suppress the global intercept, replace it with two role-specific intercepts. Its SEM analogue in wide format. Two-intercept Intermediate [Open tutorial →](two-intercept.html) ::: ::: ## How the four tutorials relate The four approaches give you the same quantities — actor and partner slopes, separated by role — but they package the model differently. - **MLM moderator (04).** A single long-format model. Gender is a factor that interacts with every predictor. The intercept is the reference-group (male) intercept; the female intercept is the reference + the gender main effect. - **SEM with moderation (05).** The same idea in `lavaan`. Manual interaction columns make the within-dyad level of the model transparent. The two-level specification places the gender interactions at the within-dyad level and the dyad-level moderators at the between-dyad level. - **SEM wide (06).** Wide format, with separate paths for the two roles. The three-model sequence (unconstrained → slopes-equal → fully constrained) is the classical Olsen & Kenny (2006) indistinguishability test. - **Two-intercept (07).** A special parameterisation that estimates both intercepts directly (rather than as reference + main effect). Useful when you want to report absolute group means. The MLM and SEM specifications should give you nearly identical estimates. The MLM is usually easier to read; the SEM gives you fit indices and the k-pattern tests for free. ## A note on the data The `dyad_data.RData` dataset has a single DGP-level gender difference: a 0.15-point gap in the male and female intercepts ($\alpha_m = 5.00$, $\alpha_f = 4.85$). The actor and partner slopes are *equal* across gender in the DGP. This means: - The [MLM moderator](mlm-moderator.html) likelihood ratio test should *not* reject the null of no gender × predictor interaction. - The [SEM wide](sem-wide.html) slope-equality test should be non-significant. - The [SEM wide](sem-wide.html) intercept-equality test *should* be significant, because the male and female intercepts differ by 0.15. This is the standard empirical pattern: dyad members are distinguishable by *means* but not by *effects*. The [two-intercept tutorial](two-intercept.html) is the recommended specification for this case.